Properties

Level $3$
Weight $0$
Character 3.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 9.29237932822 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.199598106\) \(a_{3}=+0.577350269\) \(a_{4}=+0.439035616\) \(a_{5}=+1.089395637\)
\(a_{6}=+0.692588290\) \(a_{7}=+1.027908923\) \(a_{8}=-0.672931812\) \(a_{9}=+0.333333334\) \(a_{10}=+1.306836937\)
\(a_{11}=-1.234887474\) \(a_{12}=+0.253477194\) \(a_{13}=-0.750879348\) \(a_{14}=+1.233073697\) \(a_{15}=+0.628962864\)
\(a_{16}=-1.246283344\) \(a_{17}=-0.369819063\) \(a_{18}=+0.399866035\) \(a_{19}=-0.036442338\) \(a_{20}=+0.478283485\)
\(a_{21}=+0.593463493\) \(a_{22}=-1.481368707\) \(a_{23}=+0.997637771\) \(a_{24}=-0.388517363\) \(a_{25}=+0.186782853\)
\(a_{26}=-0.900754292\) \(a_{27}=+0.192450090\) \(a_{28}=+0.451288627\) \(a_{29}=+0.617851741\) \(a_{30}=+0.754502661\)
\(a_{31}=-0.674118231\) \(a_{32}=-0.822107327\) \(a_{33}=-0.712962631\) \(a_{34}=-0.443634248\) \(a_{35}=+1.119799495\)
\(a_{36}=+0.146345205\) \(a_{37}=+1.167893600\) \(a_{38}=-0.043716160\) \(a_{39}=-0.433520802\) \(a_{40}=-0.733088980\)
\(a_{41}=-0.388923557\) \(a_{42}=+0.711917682\) \(a_{43}=-0.638475884\) \(a_{44}=-0.542159595\) \(a_{45}=+0.363131879\)
\(a_{46}=+1.196764381\) \(a_{47}=+0.238840027\) \(a_{48}=-0.719542024\) \(a_{49}=+0.056596753\) \(a_{50}=+0.224064357\)
\(a_{51}=-0.213515136\) \(a_{52}=-0.329663088\) \(a_{53}=+0.722232138\) \(a_{54}=+0.230862764\) \(a_{55}=-1.345281054\)
\(a_{56}=-0.691712613\) \(a_{57}=-0.021039993\) \(a_{58}=+0.741173777\) \(a_{59}=+0.680866864\) \(a_{60}=+0.276137099\)
\(a_{61}=+1.005379599\) \(a_{62}=-0.808670954\) \(a_{63}=+0.342636308\) \(a_{64}=+0.260084951\) \(a_{65}=-0.818005456\)
\(a_{66}=-0.855268622\) \(a_{67}=-1.388237009\) \(a_{68}=-0.162363740\) \(a_{69}=+0.575986436\) \(a_{70}=+1.343309353\)
\(a_{71}=+1.555066638\) \(a_{72}=-0.224310604\) \(a_{73}=-1.792975595\) \(a_{74}=+1.401002950\) \(a_{75}=+0.107839130\)
\(a_{76}=-0.015999484\) \(a_{77}=-1.269351880\) \(a_{78}=-0.520050733\) \(a_{79}=+1.709470246\) \(a_{80}=-1.357695637\)
\(a_{81}=+0.111111113\) \(a_{82}=-0.466551961\) \(a_{83}=+0.780225302\) \(a_{84}=+0.260551607\) \(a_{85}=-0.402879272\)
\(a_{86}=-0.765914454\) \(a_{87}=+0.356716871\) \(a_{88}=+0.830995074\) \(a_{89}=+0.477149504\) \(a_{90}=+0.435612325\)
\(a_{91}=-0.771836290\) \(a_{92}=+0.437998508\) \(a_{93}=-0.389202376\) \(a_{94}=+0.286512035\) \(a_{95}=-0.039700079\)
\(a_{96}=-0.474643843\) \(a_{97}=-0.973459725\) \(a_{98}=+0.067893266\) \(a_{99}=-0.411629151\) \(a_{100}=+0.082004481\)

Showing 100 of 5000 available coefficients

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